What is the integral of 1/(y(1+ln(y))) ?

The integral of 1/(y(1+ln(y))) is ln|1+ln(y)|+C

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integral of 1/(y(1+ln(y)))

\int \frac{1}{y ( 1 + ln ( y ) )} d y

ln ∣ 1 + ln (y) ∣ + C

Solution steps

\int \frac{1}{y ( 1 + ln ( y ) )} d y

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + ln (y)

= ln ∣ 1 + ln (y) ∣

Add a constant to the solution

= ln ∣ 1 + ln (y) ∣ + C

What is the integral of 1/(y(1+ln(y))) ?
The integral of 1/(y(1+ln(y))) is ln|1+ln(y)|+C